Sunday, October 01, 2017

Quantum Criticality in Living Systems  |  Stuart Kauffman, from the University of Calgary, and several of his colleagues have recently published a paper on the Arxiv server titled 'Quantum Criticality at the Origins of Life'. The idea of a quantum criticality, and more generally quantum critical states, comes perhaps not surprisingly, from solid state physics. It describes unusual electronic states that are are balanced somewhere between conduction and insulation. More specifically, under certain conditions, current flow at the critical point becomes unpredictable. When it does flow, it tends to do so in avalanches that vary by several orders of magnitude in size. 

Ferroelectric metals, like iron, are one familiar example of a material that has classical critical point. Above a of 1043 degrees K the magnetization of iron is completely lost. In the narrow range approaching this point, however, thermal fluctuations in the electron spins that underly the magnetic behavior extend over all length scales of the sample—that's the scale invariance we mentioned. In this case we have a continuous phase transition that is thermally driven, as opposed to being driven by something else like external pressure, magnetic field, or some kind of chemical influence.

Quantum criticality, on the other hand, is usually associated with stranger electronic behaviors—things like high-temperature superconductivity or so-called heavy fermion metals like CeRhIn5. One strange behavior in the case of heavy fermions, for example, is the observation of large 'effective mass'—mass up to 1000 times normal—for the conduction electrons as a consequence of their narrow electronic bands. These kinds of phenomena can only be explained in terms of the collective behavior of highly correlated electrons, as opposed to more familiar theory based on decoupled electrons. 

Experimental evidence for critical points in of materials like CeRhIn5 has only recently been found. In this case the so-called "Fermi surface," a three-dimensional map representing the collective energy states of all electrons in the material, was seen to have large instantaneous shifts at the critical points. When electrons across the entire Fermi surface are strongly coupled, unusual physics like superconductivity is possible.

The potential existence of in proteins is a new idea that will need some experimental evidence to back it up. Kauffman and his group eloquently describe the major differences between current flow in proteins as compared to metallic conductors. They note that in metals charges 'float' due to voltage differences. Here, an electric fields accelerate electrons while scattering on impurities dissipates their energy fixing a constant average propagation velocity.
By contrast, this kind of a mechanism would appear to be uncommon in biological systems. The authors note that charges entering a critically conducting biomolecule will be under the joint influence of the quantum Hamiltonian and the excessive decoherence caused by the environment. Currently a huge focus in Quantum biology, this kind of conductance has been seen for example, for excitons in the light-harvesting systems. As might already be apparent here, the logical flow of the paper, at least to nonspecialists, quickly devolves into the more esoteric world of quantum Hamiltonians and niche concepts like 'Anderson localization.' 

To try to catch a glimpse of what might be going on without becoming steeped in formalism I asked Luca Turin, who actually holds the patent for semiconductor structures using proteins as their active element, for his take on the paper. He notes that the question of how electrons get across proteins is one of the great unsolved problems in biophysics, and that the Kauffman paper points in a novel direction to possibly explain conduction. Quantum tunnelling (which is an essential process, for example, in the joint special ops of proteins of the respiratory chain) works fine over small distances. However, rates fall precipitously with distance. Traditional hole and electron transport mechanisms butt against the high bandgap and absence of obvious acceptor impurities. Yet at rest our body's fuel cell generates 100 amps of electron current.
In suggesting that biomolecules, or at least most of them, are quantum critical conductors, Kauffman and his group are claiming that their electronic properties are precisely tuned to the transition point between a metal and an insulator. An even stronger reading of this would have that there is a universal mechanism of charge transport in living matter which can exist only in highly evolved systems. To back all this up the group took a closer look at the electronic structure of a few of our standard issue proteins like myoglobin, profilin, and apolipoprotein E.

In particular, they selected NMR spectra from the Protein Data Bank and used a technique known as the extended Huckel Hamiltonion method to calculate HOMO/LUMO orbitals for the proteins. For more comments on HOMO/LUMO orbital calculations you might look at our post on Turin's experiments on electron spin changes as a potential general mechanism of anesthesia. To fully appreciate what such calculations might imply in this case, we have to toss out another fairly abstract concept, namely, Hofstadter's butterfly as seen in the picture below.